यदि ` x= (3at )/(1+t^(3) )` तथा ` y=(3at ^(2))/(1+t^(3))` तो ` (dy)/(dx)` का मान ज्ञात कीजिए|

Explanation

दिया है -` x= (3at )/(1+t^(3))` तथा ` y= (3at ^(2))/(1+t^(3))`
` rArr " "(dx)/(dt) =(3a*(1+t^(3) )*(d)/(dt) *t-3at *(d)/(dt)(1+t^(3)))/((1+t^(3) )^(2))`
` =(3a (1+t^(3))*1-3at *3t^(2))/((1+t^(3))^(2))`
` " "= 3a ((1-2t^(3))/((1+t^(3) )^(2)))" "...(1)`
इसी प्रकार ` " "y= 3a *(t^(2))/(1+t^(3))`
`rArr(dy)/(dt)=3a *((1+t^(3))(d)/(dt) t^(2) -t^(2)*(d)/(dt) (1+t^(3)))/((1+t^(3))^(2))`
` " "=3a ((1+t^(3) )*2t -t^(2) *3t^(2))/((1+t^(3))^(2) )= 3a (t*(2-t^(3)))/((1+t^(3))^(2))`
अतः ` (dy)/(dx) =(dy//dt)/(dx//dt)=(3at (2-t^(3)))/((1+t^(3))^(2))xx((1+t^(3))^(2))/(3a(1-2t^(3)))`
` " "(dy)/(dx)=(t(2-t^(3)))/(1-2t^(3))`